The invention is directed to a brake booster combined with an anti-skid apparatus as generally defined hereinafter. Such a brake booster with an anti-skid apparatus for the generation of brake pressure and automatic brake pressure modulation in intrinsically safe closed brake circuits was already proposed by the copending U.S. patent application Ser. No. 788,320 filed Oct. 17, 1985. By means of coupling its brake valve to the tappet and the booster piston the latter travels approximately the same distance as the tappet during brake boost, so that the displacement travel of the booster piston is generally proportional to brake pedal travel. If brake booster is not present, the booster piston is mechanically moved via the tappet. For the purpose of this the tappet first travels through a very short idle stroke occasioned for structural reasons which, for all practical purposes, cannot be felt in the brake pedal. After that the tappet and the booster piston travel equal distances so that, if brake boost is missing, the brake pedal travel connected with a certain brake pressure cannot be differentiated from that needed when brake boost is present. If there is danger of skidding, the booster piston is directed into the direction of the tappet by means of the valve arrangement which results, in the usual way, in reductions in the brake pressure, for instance down to a zero value. If the brake pressure losses exceed a preset value sudden very hard reactions of the brake pedal occur. This may irritate an unsure driver to the extent that he may decrease foot pressure on the brake pedal in a detrimental manner.